The present invention addresses the following direction finding problem: given voltage measurements at N antenna ports, find the angle of arrival of an emitter source without a priori knowledge of its polarization. That is a four dimensional identification problem. There are two angle parameters and two polarization parameters. Previously known direction finding algorithms have been devised for implementation by simple analog hardware. As a result the algorithms are simple but depend highly upon the design and tolerances of the antenna system and use limited calibration data and computations. Four lobe monopulse antennas, two plane interferometers, and multimode spiral antennas are examples of hardware that use simple direction finding algorithms. The accuracy of most current direction finding techniques depends upon the accuracy of the hardware in meeting the design requirements. For example, accurate direction finding using monopulse antennas and interferometers requires that the elements have identical responses, i.e., low cross-polarization response. Large costs are required to ensure that the hardware meets that requirement. Often performance is compromised, inasmuch as the hardware cannot meet the response requirements over all angles of space and polarizations. That is particularly true of the installed performance where the beams in space are influenced by the installation surroundings.
The accuracy of direction finding using a four lobe monopulse antenna is limited by the amplitude and phase balance of the excitation of the four sub-apertures and by the cross-polarization in the sum beam region. In the side lobe region direction finding using a four lobe monopulse antenna can yield ambiguities. Thus a broad beam guard antenna is typically used to discriminate between the main beam region and the side lobe region. That approach yields additional challenges in designing a guard antenna without punch-through and polarization response equal to that of the sum beam. The accuracy of direction finding using interferometers is limited by element-to-element phase errors and the fact that all elements do not have the same polarization response. Interferometer installation effects cause these accuracy limitations in many cases. Direction finding accuracy from multimode spirals are limited by the element and mode former tolerances. It is assumed that each arm yields the same antenna response rotated by the proper angle (360 degrees divided by the number of arms). In each of these examples it is desired that each antenna port (mode) have the same polarization at any given angle of space. If indeed all ports are polarization matched, the direction finding problem is greatly simplified to a two-dimensional (two angles only) identification problem. The penalty is that the antenna system cannot receive cross-polarized signals and thus direction finding cannot be obtained for all emitting sources. Another general observation about previously known direction finding techniques is that they typically do not use all of the available information. With the availability of low cost computing, limited space for antennas, and the need for increased accuracy over wider bands for all polarizations, new direction finding techniques are needed.